"Logi tech M650 wireless mouse not detected by MacBook Air: I bought a new MacBook Air and am trying to connect my M650 mouse. It has both Unifying and Bolt receivers. I used it on my previous old MacBook Pro. I don't want to use the USB device. The M650 is not located."
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Connecting a Bluetooth Mouse:
A. Compatibility:
This device is compatible with macOS 10.10 and later. So, it should work, if you can see it: m650 Signature Wireless Mouse - Logitech
B. Forget the Mouse on the Old Mad:
Forget the mouse on your old Mac. Then, see if you can see it and connect to it.
Go Here: Connect a Bluetooth Device with your Mac - Apple Support